Theorem: Coarse continuum domain of dependence

If a matched modification pair has

then its two complete report laws agree.

Proof. Every discrete dependency path obeys the physical bound in Proposition prop:C2b. Report acquisition events converge to $R$, and modified footprints approach $K^{\prime }$. The positive margin therefore places every modified gate outside the ancestor subnetwork of the report ports for all sufficiently large $n$. Their initial inputs and included gates agree. Apply Theorem thm:order to the full report tuple, then pass to the total-variation limit.